Report Number: CS-TR-77-604
Institution: Stanford University, Department of Computer Science
Title: Control of the dissipativity of Lax-Wendroff type methods for
first order systems or hyperbolic equations
Author: Chan, Tony Fan C.
Author: Oliger, Joseph
Date: March 1977
Abstract: Lax-Wendroff methods for hyperbolic systems have two
characteristics which are sometimes troublesome. They are
sometimes too dissipative -- they may smooth the solution
excessively -- and their dissipative behavior does not affect
all modes of the solution equally. Both of these difficulties
can be remedied by adding properly chosen accretive terms. We
develop modifications of the Lax-Wendroff method which
equilibrate the dissipativity over the fundamental modes of
the solution and allow the magnitude of the dissipation to be
controlled. We show that these methods are stable for the
mixed initial boundary value problem and develop analogous
formulations for the two-step Lax-Wendroff and MacCormack
methods.
http://i.stanford.edu/pub/cstr/reports/cs/tr/77/604/CS-TR-77-604.pdf